%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET691+4 : TPTP v3.4.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:35:55 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 41 ( 17 ~; 17 |; 7 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-3 aty)
% Number of variables : 15 ( 3 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(subset,plain,
! [A,B,C] :
( ( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) )
& ( ~ member(x(A,B,C),B)
| subset(A,B) )
& ( member(x(A,B,C),A)
| subset(A,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET691+4.tptp',unknown),
[] ).
cnf(144861168,plain,
( member(x(A,B,C),A)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subset]),
[] ).
fof(empty_set,plain,
! [A] : ~ member(A,empty_set),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET691+4.tptp',unknown),
[] ).
cnf(144961000,plain,
~ member(A,empty_set),
inference(rewrite,[status(thm)],[empty_set]),
[] ).
cnf(155638456,plain,
subset(empty_set,A),
inference(resolution,[status(thm)],[144861168,144961000]),
[] ).
fof(thI16,plain,
( ( equal_set(a,empty_set)
| subset(a,empty_set) )
& ( ~ subset(a,empty_set)
| subset(a,empty_set) )
& ( equal_set(a,empty_set)
| ~ equal_set(a,empty_set) )
& ( ~ subset(a,empty_set)
| ~ equal_set(a,empty_set) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET691+4.tptp',unknown),
[] ).
cnf(145142552,plain,
( equal_set(a,empty_set)
| subset(a,empty_set) ),
inference(rewrite,[status(thm)],[thI16]),
[] ).
fof(equal_set,plain,
! [B,A] :
( ( subset(B,A)
| ~ equal_set(A,B) )
& ( subset(A,B)
| ~ equal_set(A,B) )
& ( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET691+4.tptp',unknown),
[] ).
cnf(144899768,plain,
( subset(A,B)
| ~ equal_set(A,B) ),
inference(rewrite,[status(thm)],[equal_set]),
[] ).
cnf(145136608,plain,
~ equal_set(a,empty_set),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[thI16,144899768]),
[] ).
cnf(155853144,plain,
subset(a,empty_set),
inference(resolution,[status(thm)],[145142552,145136608]),
[] ).
cnf(144893104,plain,
( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ),
inference(rewrite,[status(thm)],[equal_set]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[155638456,155853144,144893104,145136608]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(subset,plain,(((~subset(A,B)|~member(C,A)|member(C,B))&(~member(x(A,B,C),B)|subset(A,B))&(member(x(A,B,C),A)|subset(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET691+4.tptp',unknown),[]).
%
% cnf(144861168,plain,(member(x(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[subset]),[]).
%
% fof(empty_set,plain,(~member(A,empty_set)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET691+4.tptp',unknown),[]).
%
% cnf(144961000,plain,(~member(A,empty_set)),inference(rewrite,[status(thm)],[empty_set]),[]).
%
% cnf(155638456,plain,(subset(empty_set,A)),inference(resolution,[status(thm)],[144861168,144961000]),[]).
%
% fof(thI16,plain,(((equal_set(a,empty_set)|subset(a,empty_set))&(~subset(a,empty_set)|subset(a,empty_set))&(equal_set(a,empty_set)|~equal_set(a,empty_set))&(~subset(a,empty_set)|~equal_set(a,empty_set)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET691+4.tptp',unknown),[]).
%
% cnf(145142552,plain,(equal_set(a,empty_set)|subset(a,empty_set)),inference(rewrite,[status(thm)],[thI16]),[]).
%
% fof(equal_set,plain,(((subset(B,A)|~equal_set(A,B))&(subset(A,B)|~equal_set(A,B))&(equal_set(A,B)|~subset(A,B)|~subset(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET691+4.tptp',unknown),[]).
%
% cnf(144899768,plain,(subset(A,B)|~equal_set(A,B)),inference(rewrite,[status(thm)],[equal_set]),[]).
%
% cnf(145136608,plain,(~equal_set(a,empty_set)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[thI16,144899768]),[]).
%
% cnf(155853144,plain,(subset(a,empty_set)),inference(resolution,[status(thm)],[145142552,145136608]),[]).
%
% cnf(144893104,plain,(equal_set(A,B)|~subset(A,B)|~subset(B,A)),inference(rewrite,[status(thm)],[equal_set]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[155638456,155853144,144893104,145136608]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------